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contrapositives

samirakhafasamirakhafa Alum Member
edited September 2018 in General 64 karma

Hey guys, i have a pretty simple question. How would you read the contrapositive of this chain:

A Some B---> C?

Thanks! :)

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  • NotMyNameNotMyName Alum Member Sage ⭐
    5320 karma

    You can't contrapose a some-statement because it's largely undefined. We know that some As are Bs, but it could be that 1% of As are Bs or that 100% of As are Bs.

  • samirakhafasamirakhafa Alum Member
    64 karma

    so would we just read that chain as ~C--->~B

  • keets993keets993 Alum Member ⭐ ⏰ 🍌
    6045 karma

    A Some B---> C?

    The only way you can read this chain is as A some B -> C. You can conclude that A some C. You can also read it as B some A, if you prefer. But intersectional relationships ("some," "most" and "few") don't have contrapositives.

    Essentially, since these relationships consist of a range as opposed to a fix number (none, all) you can't really come up with an equivalent contrapositive. If I say some apples are red then you don't know if I mean one apple is red or all apples are red or 33% of apples are red. If we don't know the starting number we can't really contrapose it. Furthermore, if you try to contrapose it the same we do with conditional logic you would get something like, "some red things are not apples". However, that is not the logical equivalent of "some apples are red" because while we are discussing red things, it is in relationship to apples. We know nothing about the entire group of red things based off of the information we are provided and so it doesn't work. Similarily, if we say that some apples are not red...that could very well be true provided our original statement because we don't know how many of apples are red. If 99 are red, 1 could not be red and so it would not be the contrapositive.

    so would we just read that chain as ~C--->~B

    It's true that based off of the statement "B -> C" that the contrapositive of that statement alone would be "/C -> /B" but it's not the contrapositve of the statement "A some B -> C"

    Similarily, you can't say /C -> /B....some A. Or that /B some /A. Because we don't know anything about /B in relation to A. We only know the relationship that exists between A some B.

    Hope that helps.

  • NotMyNameNotMyName Alum Member Sage ⭐
    5320 karma

    @keets993 NAAAIIIIILED IT.

  • AudaciousRedAudaciousRed Alum Member
    edited September 2018 2689 karma

    The reason you can't get a contrapositive is because you don't know what "some" is. Maybe it turns out that some is ALL. Maybe some is just 2. Maybe some is Most of them/it. The opposite of "some" is "not some". But since we don't know what "some" means from the get go, we can't say what "not some" might be. Since we don't know, we can't accurately make an opposite to this. It's just too wide of a possibility.

  • samirakhafasamirakhafa Alum Member
    64 karma

    Thanks a lot guys. That was really helpful!!

  • samantha.ashley92samantha.ashley92 Alum Member
    1777 karma

    I would review the "some and most relationships" part of the CC, as well as invalid argument forms. It's always good to brush up on the fundamentals. I actually plan on reviewing advanced bi-conditionals and advanced logic today. The last thing I want to do is stay rusty because I rarely practice it. When this stuff comes up in PTs, I think, "I used to know this", and it takes me way longer than it should to figure this stuff out.

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